Rough hand-written Lecture Notes can be found here, here and here.

Problem Sheets in PDF: Sheet 1 Sheet 2 Sheet 3 Sheet 4 Sheet 5 Sheet 6 Sheet 7 Sheet 8 Sheet 9

Solutions to sheet 8 (by Robert Cronin (croninro@tcd.ie)).

Most solutions to the exercises are very similar to those older ones that can be found here, here and here and here. Solutions to the last two exercises from 2015 are here.

Course outline:

**Linear Algebra: Chapters 3-6 (11th and 10th edition) or 3-7 (9th edition) in
Anton-Rorres' book "Elementary Linear Algebra (with applications)".** Euclidean n-Space and n-Vectors, Operations with them. Linear Transformations and their Matrices. Subspaces. Linear Combinations of Vectors. Subspaces spanned by a Set of Vectors. Linear Independence of a Set of Vectors. Basis and Dimension. Standard Basis in n-space. Coordinates of Vectors relative to a Basis. General and Particular Solutions for a Linear System. Row, Column and Nullspace of a Matrix. Finding Bases for them using Elementary Row Operations. Rank and Nullity of a Matrix. Inner Products, Lengths, Distances and Angles relative to them. Orthogonal and Orthonormal Bases relative to an Inner Product. Orthogonal projections to Subspaces. Gram-Schmidt Process (see Example 7 in Chapter 6.3). Eigenvalues and Eigenvectors of Square Matrices.

**Fourier Analysis (Chapter 10 (or 11 in 9th ed.) in Kreyszig' book "Advanced Engineering Mathematics").** Fourier Series for periodic functions. Euler Formulas for the Fourier Coefficients. Even and Odd Functions. Fourier Cosine and Fourier Sine Series for them. Fourier Integral and Fourier Transform.

Beautiful Fourier series visualisation with d3.js

Calculus for Beginners and Artists by Daniel Kleitman

Multivariable Calculus Online by Jeff Knisley

Taylor's formula, linear and quadratic approximations by Eric A. Carlen

Working with Vectors (A Self-Help Workbook for Science and Engineering Students by Jenny Olive)

Linear Algebra Toolkit by Przemyslaw Bogacki

Java applet introducing 3-vectors by Maths Online

Matrix Algebra Tutorials by S.O.S. MATHematics

A Linear Algebra book by Jim Hefferon (PDF file)

Importance of Linear algebra in Engineering Design Methodology by Mysore Narayanan (PDF file)

Beautiful WebGL water simulation by Evan Wallace and the author's article about it

2E01 2015 by Dmitri Zaitsev with Problem Sheets.

2E02 2015 by Dmitri Zaitsev with Problem Sheets.

2E02 2014 by Dmitri Zaitsev with Problem Sheets.

2E02 2013 by Dmitri Zaitsev with Problem Sheets.

2E02 2012 by Dmitri Zaitsev with Problem Sheets.

2E02 2011 by Dmitri Zaitsev with Problem Sheets.

2E02 2010 by Dmitri Zaitsev with Problem Sheets.

2E2 2008-09 by Dmitri Zaitsev with Problem Sheets and some Solutions.

2E2 2007-08 by Dmitri Zaitsev with Problem Sheets and some Solutions.

2E1 2006-07 Part I by Richard Timoney and Part II by Dmitri Zaitsev with Problem Sheets and some Solutions.

2E1 2005-06 by Dmitri Zaitsev with Problem Sheets and some Solutions.

2E1 2004-05 by Dmitri Zaitsev with Problem Sheets and some Solutions.

2E1 2003-04 by Fermin Viniegra with many interesting links.

**Past examinations:**

TCD examination papers (2012 - present)

TCD examination papers (1998 - 2012)

School of Mathematics examination papers (1992 - 2000)

For Scholarship exam related problems see also years 2009 and 2008 papers.

I will appreciate any (also critical) suggestions that you may have for the next term. Let me know your opinion, what can/should be improved, avoided etc. and I will do my best to follow them. Please use the feedback form from where you can also send anonymous messages.